Space of modular forms of level 612, weight 2, and Character 612.w

• Label: 612.2.w
• Level: $612$
• Weight: $2$
• Character orbit: 612.w
• Rep. character: $\chi_{612}(145,\cdot)$
• Character field: $\Q(\zeta_{8})$
• Dimension: $28$
• Newform subspaces: $3$
• Sturm bound: $216$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 612 = 2^{2} \cdot 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	612.w (of order \(8\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 17 \)
Character field:			\(\Q(\zeta_{8})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(216\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(612, [\chi])\).

	Total	New	Old
Modular forms	480	28	452
Cusp forms	384	28	356
Eisenstein series	96	0	96

Trace form

28 * q + 4 * q^5 - 12 * q^17 - 4 * q^19 - 16 * q^23 - 4 * q^25 + 12 * q^29 - 24 * q^31 + 32 * q^35 + 4 * q^37 + 28 * q^41 + 36 * q^43 + 12 * q^49 + 4 * q^53 + 60 * q^59 + 20 * q^61 + 24 * q^65 + 32 * q^67 - 16 * q^71 - 20 * q^73 - 28 * q^77 - 8 * q^79 + 4 * q^83 - 12 * q^85 - 24 * q^91 - 100 * q^95 - 36 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(612, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
612.2.w.a	$612$	$2$	612.w	17.d	$8$	$4$	$1$	$4.887$	\(\Q(\zeta_{8})\)	None					68.2.h.a	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{8}]$	\(q+(-1+\zeta_{8})q^{5}+(\zeta_{8}+\zeta_{8}^{2})q^{7}+(2+\cdots)q^{11}+\cdots\)
612.2.w.b	$612$	$2$	612.w	17.d	$8$	$8$	$2$	$4.887$	8.0.\(\cdots\).13	None		✓			612.2.w.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{8}]$	\(q-\beta _{5}q^{5}+(\beta _{2}+\beta _{4})q^{7}+(\beta _{1}-\beta _{5}+\beta _{7})q^{11}+\cdots\)
612.2.w.c	$612$	$2$	612.w	17.d	$8$	$16$	$4$	$4.887$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None			✓		204.2.o.a	$2$	$0$	\(0\)	\(0\)	\(8\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{8}]$	\(q+(-1-2\beta _{2}-\beta _{4}+\beta _{5}+\beta _{9}+\beta _{10}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(612, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(612, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(17, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(34, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(51, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(68, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(102, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(153, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(204, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(306, [\chi])\)\(^{\oplus 2}\)